Did my kitten get cold after a bath?

Hello,
I have 2 kitten Niki (black) and Nico (Tabby) and they are 10 and 13weeks old.

However Niki has really bad habit of handling his stool and always mess all those brown stuff all over himself while trying to bury them. I decided to give him a quick warm bath but then the next day I found out some discharge on the right eye only.

Nico had flu nearly month ago and now fully recovered and I don't believe he had passed it on to Niki.

My question is he is sick now or something else has caused the problem? I know bringing him to the vet is the best but I know the vet is gonna give the same prescription and it's very costly to do so (visited the vet 3 times already in December).

Can I use those medicine previously left over by Nico which are antibiotics panacur 10% to treat Niki?

Many thanks